WO2021042621A1

WO2021042621A1 - Linear equalization method and apparatus for orthogonal time frequency space system, and electronic device and storage medium

Info

Publication number: WO2021042621A1
Application number: PCT/CN2019/125475
Authority: WO
Inventors: 许文俊; 邹婷婷; 高晖; 别志松; 张平; 林家儒
Original assignee: 北京邮电大学
Priority date: 2019-09-02
Filing date: 2019-12-16
Publication date: 2021-03-11
Also published as: US20220182265A1; CN110730145B; CN110730145A

Abstract

A linear equalization method and apparatus for an orthogonal time frequency space (OTFS) system, an electronic device for realizing the method, and a computer-readable storage medium. The method comprises: determining an effective channel matrix of an OTFS system in a delay-Doppler domain under a rectangular window limitation condition (202); determining a linear equalization estimation matrix according to the effective channel matrix (204); and equalizing received sampling signals according to the linear equalization estimation matrix (206).

Description

正交时频空***线性均衡方法、装置、电子设备及存储介质Orthogonal time-frequency-space system linear equalization method, device, electronic equipment and storage medium

本申请基于申请号为201910847083.0，申请日为2019年9月2日的中国专利申请提出，并要求该中国专利申请的优先权，该中国专利申请的全部内容在此引入本申请作为参考。This application is filed based on a Chinese patent application with an application number of 201910847083.0 and an application date of September 2, 2019, and claims the priority of the Chinese patent application. The entire content of the Chinese patent application is hereby incorporated into this application by reference.

技术领域Technical field

本发明涉及无线通信技术领域，特别是指一种正交时频空***线性均衡方法、装置、电子设备以及计算机可读存储介质。The present invention relates to the field of wireless communication technology, and in particular to a linear equalization method, device, electronic equipment, and computer-readable storage medium for an orthogonal time-frequency-space system.

背景技术Background technique

正交频分复用技术(Orthogonal Frequency Division Multiplexing，OFDM)因为其高频谱效率等优势在5G中被广泛采用，但是当用户移动时，由于多普勒效应的出现，子载波间的正交性被破坏，这将导致载波间干扰，因此***通信性能下降。Orthogonal Frequency Division Multiplexing (OFDM) is widely used in 5G due to its advantages such as high spectrum efficiency, but when users move, due to the Doppler effect, the orthogonality between sub-carriers If it is destroyed, it will cause inter-carrier interference, so the system communication performance will decrease.

正交时频空调制(Orthogonal Time Frequency Space，OTFS)是一种新型的调制方式，可以利用时延-多普勒域信道不随时间变化的特点有效抵抗信道由于多普勒效应导致用户间通信性能下降的问题。具体来讲，OTFS***将发送信息承载在时延-多普勒域，在发射端通过逆辛有限傅里叶变换(Inverse Symplectic Finite Fourier Transform，ISFFT)，将每一个时延-多普勒域信息符号拓展至一定范围内的整个时频域，进而保证OTFS帧内的每一个符号都经历一个相对稳定的信道，也即将一个双色散的信道转化为一个几乎无频率/时间色散的信道。在接收端，OTFS***通过辛有限傅里叶变换(Symplectic Finite Fourier Transform，ISFFT)，将时频域的信息转换到时延-多普勒域进而进行均衡解调等操作。因此，OTFS作为一种新型多载波调制技术，能够有效对抗高动态的通信信道环境，展现出对高多普勒拓展的强鲁棒性。Orthogonal Time Frequency Space (OTFS) is a new type of modulation method that can effectively resist the communication performance between users caused by the Doppler effect due to the time delay-Doppler domain channel does not change with time. The problem of falling. Specifically, the OTFS system carries the transmission information in the delay-Doppler domain, and uses the Inverse Symplectic Finite Fourier Transform (ISFFT) at the transmitting end to convert each delay-Doppler domain. The information symbols are extended to the entire time-frequency domain within a certain range, thereby ensuring that each symbol in the OTFS frame experiences a relatively stable channel, that is, converting a dual-dispersion channel into a channel with almost no frequency/time dispersion. At the receiving end, the OTFS system uses Symplectic Finite Fourier Transform (ISFFT) to convert information in the time-frequency domain into the time-delay-Doppler domain to perform operations such as equalization and demodulation. Therefore, OTFS, as a new type of multi-carrier modulation technology, can effectively combat the highly dynamic communication channel environment and exhibit strong robustness to high Doppler expansion.

由于时延-多普勒域信道的稀疏特性，现有的大部分对OTFS通信***信道均衡的研究多集中在利用信道稀疏性进行非线性均衡，而对于线性均衡方法的研究较少。然而，在实际***的应用中，相比于线性均衡的方式，非线性均衡方法复杂度很高，因此实用性低。此前，在现有另一些均衡方案中均以无限窗函数条件和理想信道条件为前提进行均衡，但这样的前提条件在实际***中是不可能实现的，导致这些均衡方案的实际应用性较低。Due to the sparse nature of the delay-Doppler domain channel, most of the existing research on channel equalization in OTFS communication systems focuses on the use of channel sparsity for nonlinear equalization, and there are few studies on linear equalization methods. However, in the application of actual systems, compared with the linear equalization method, the nonlinear equalization method is more complicated and therefore has low practicability. Previously, in other existing equalization schemes, infinite window function conditions and ideal channel conditions were used as the premise for equalization, but such preconditions were impossible to achieve in actual systems, resulting in low practical applicability of these equalization schemes. .

发明内容Summary of the invention

有鉴于此，本申请的实施例提出一种OTFS***线性均衡方法、装置、电子设备以及计算机可读存储介质。In view of this, the embodiments of the present application propose a linear equalization method, device, electronic device, and computer-readable storage medium for an OTFS system.

本申请实施例所述的OTFS***线性均衡方法包括：确定所述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵；根据所述有效信道矩阵确定线性均衡评估矩阵；以及根据上述线性均衡评估矩阵对接收的采样信号进行均衡。The linear equalization method of the OTFS system according to the embodiment of the present application includes: determining the effective channel matrix of the OTFS system in the delay-Doppler domain under the restriction of the rectangular window; determining the linear equalization evaluation matrix according to the effective channel matrix; and The received sampling signal is equalized according to the above linear equalization evaluation matrix.

在本申请的实施例中，上述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵H _eff为由N×N个循环小矩阵A _n组成的块循环矩阵，其中，循环小矩阵A _n根据时域信道矩阵确定；以及所述确定所述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵包括：根据时域信道矩阵

确定组成上述有效信道矩阵的循环小矩阵A _n；以及根据所述循环小矩阵A _n确定所述有效信道矩阵H _eff。 In an embodiment of the present application, in the above-mentioned rectangular window OTFS system delay constraints - the effective channel matrix H _eff Doppler domain by N × N matrix A _n cycles small block-circulant matrices, wherein the loop small matrix a _n is determined according to the time-domain channel matrix; and determining the time delay of the system limits OTFS under conditions of a rectangular window - the effective channel matrix Doppler domain comprises: time-domain channel matrix

Determining the composition of the effective channel matrix of small cyclic matrix A _n; and determining the effective channel matrix H _eff according to the cyclic submatrix A _n.

在本申请的实施例中，上述根据时域信道矩阵

确定组成上述有效信道矩阵的循环小矩阵A _n包括：根据如下表达式确定所述循环小矩阵A _n： In the embodiment of the present application, the above is based on the time-domain channel matrix

Determining the composition of the effective channel matrix A _n cyclic submatrix comprising: a cyclic submatrix A _n is determined according to the following expression:

其中，

表示所述时域信道矩阵

中第p个OFDM符号经过的时域信道矩阵；矩阵

是一个NM×NM的块对角方阵，表示循环前缀的长度大于信道的最大时延条件下的时域信道矩阵；以及运算符FFT _Mtx()表示对一系列矩阵进行快速傅里叶变换操作，变换得到的结果也是一系列矩阵。 among them,

Represents the time domain channel matrix

The matrix of the time-domain channel through which the p-th OFDM symbol passes through; matrix

It is an NM×NM block diagonal square matrix, which means that the length of the cyclic prefix is greater than the time domain channel matrix under the maximum delay of the channel; and the operator FFT _Mtx () means fast Fourier transform operation on a series of matrices , The result of the transformation is also a series of matrices.

在本申请的实施例中，上述根据所述循环小矩阵A _n确定所述有效信道矩阵H _eff包括：根据如下表达式确定所述有效信道矩阵H _eff： In an embodiment of the present disclosure, the determination of the effective channel matrix H _eff comprising the said cyclic submatrix A _n: determining the effective channel matrix H _eff according to the following expression:

在本申请的实施例中，上述线性均衡评估矩阵包括：迫零均衡评估矩阵W _ZF；其中，所述根据所述有效信道矩阵确定线性均衡评估矩阵包括：对所述循环小矩阵A _n进行逆快速傅里叶变换得到中间矩阵S _t；对所述中间矩阵S _t求逆；对求逆后的中间矩阵S _t ^-1进行快速傅里叶变换得到迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q；以及根据迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q确定迫零均衡评估矩阵W _ZF。 In an embodiment of the present application, the above-described evaluation matrix linear equalizer comprising: a zero-forcing equalization evaluation matrix W _ZF; wherein said determining comprises linear equalization matrix based on the effective assessment channel matrix: the matrix A _n cyclic small inverse fast Fourier transform intermediate matrix S _T; S _T of the intermediate matrix inversion; intermediate matrix S _t ^-1 the inverse fast Fourier transform to obtain a second cycle zero-forcing equalization of the evaluation matrix W _ZF The small matrix B _q ; and the zero-forcing equalization evaluation matrix W _ZF is determined according to the second circulant small matrix B _q of the zero-forcing equalization evaluation matrix W _ZF .

在本申请的实施例中，上述对求逆后的中间矩阵S _t ^-1进行快速傅里叶变换得到迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q包括：根据如下表达式，确定所述迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q： In the embodiment of the present application, the _{fast Fourier transform performed on the intermediate matrix S t} ^-1 after the inversion to obtain the second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF includes: Determine according to the following expression The second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF :

其中，B _q，

Among them, B _q ,

在本申请的实施例中，上述线性均衡评估矩阵包括：最小均方差均衡的评估矩阵W _MMSE；其中，所述根据所述有效信道矩阵确定线性均衡评估矩阵包括：根据所述有效信道矩阵及其转置以及信道噪声的方差，确定第二中间矩阵；对所述第二中间矩阵求逆；对所述求逆后的第二中间矩阵与有效信道矩阵的转置矩阵相乘得到最小均方差均衡评估矩阵W _MMSE。 In an embodiment of the present application, the above linear equalization evaluation matrix includes: a minimum mean square error equalization evaluation matrix W _MMSE ; wherein, determining the linear equalization evaluation matrix according to the effective channel matrix includes: according to the effective channel matrix and its Transpose and the variance of the channel noise, determine the second intermediate matrix; invert the second intermediate matrix; multiply the inverted second intermediate matrix and the transposed matrix of the effective channel matrix to obtain the minimum mean square error equalization Evaluation matrix W _MMSE .

在本申请的实施例中，上述确定第二中间矩阵包括：根据如下表达式确定所述第二中间矩阵：In the embodiment of the present application, the foregoing determining the second intermediate matrix includes: determining the second intermediate matrix according to the following expression:

其中，[·] _N为取模操作，[N] _N＝N； Among them, [·] _N is the modulo operation, [N] _N ＝N;

所述对所述第二中间矩阵求逆包括：根据如下表达式对所述第二中间矩阵求逆：The inverting the second intermediate matrix includes: inverting the second intermediate matrix according to the following expression:

对所述求逆后的第二中间矩阵与有效信道矩阵的转置矩阵相乘得到最小均方差均衡评估矩阵W _MMSE包括：根据如下表达式确定所述最小均方差均衡评估矩阵W _MMSE： Multiplying the inverted second intermediate matrix and the transposed matrix of the effective channel matrix to obtain the minimum mean square error equalization evaluation matrix W _MMSE includes: determining the minimum mean square error equalization evaluation matrix W _MMSE according to the following expression:

在本申请的实施例中，设所述中间矩阵或所述第二中间矩阵为S _t；所述对所述中间矩阵求逆或所述对所述第二中间矩阵求逆包括： In the embodiment of the present application, it is assumed that the intermediate matrix or the second intermediate matrix is S _t ; the inverting the intermediate matrix or the second intermediate matrix includes:

对运算辅助参量进行初始化定义，定义L矩阵与U矩阵分别为L＝I _M，U＝0 _M，定义中间变量矩阵Y＝0 _M，将信道的多径时延表示为向量d _chan＝[D ₁，D ₂，D ₃，…，D _P]，其中P表示多径的数量，D ₁，D ₂，D ₃，…，D _P是在多径时延在时延-多普勒平面上时延轴上的坐标值，定义辅助向量d＝[d _chan，M-D _P]； Initialize the definition of the auxiliary parameters of the operation, define the L matrix and the U matrix as L = I _M , U = 0 _M , define the intermediate variable matrix Y = 0 _M , and express the multipath delay of the channel as a vector d _chan =[D ₁ , D ₂ , D ₃ ,..., D _P ], where P represents the number of multipaths, D ₁ , D ₂ , D ₃ ,..., D _P is the multipath delay on the delay-Doppler plane The coordinate value on the time delay axis defines the auxiliary vector d=[d _chan , MD _P ];

求解L矩阵的前M-D _P列：L(i+D _P，i)＝S _t(i+D _P，i)/S _t(i，i)；其中，L(i+D _P，i)表示L矩阵中的i+D _P行i列位置上的元素，i为循环变量，i＝1：M-D _P； Solve the first MD _P column of the L matrix: L(i+D _P ,i)=S _t (i+D _P ,i)/S _t (i,i); where L(i+D _P ,i) means The element at the row i column position of i+D _P in the L matrix, i is the loop variable, i=1: MD _P ;

求解U矩阵的前M-D _P行：

其中，U(ξ，：)和S _t(ξ，：)分别表示U矩阵和S _t矩阵的第ξ行，向量ξ从D _p+1逐一增加到D _p+1，其中，p为循环变量，p＝1：P+1； Solve the first MD _P rows of the U matrix:

Among them, U(ξ,:) and _St (ξ,:) represent _{the ξth row of U matrix and St} matrix respectively, and the vector ξ _{increases from D p} +1 to D _p+1 one by one, where p is the cyclic variable , P=1: P+1;

求解L矩阵的后D _P列和U矩阵的后D _P行，利用通用的LU分解方法求解，最后得到矩阵S _t的LU分解结果即L和U； After solving the row D _P D _P L columns of the matrix and the U matrix, LU decomposition using a general method to solve the last matrix S _t to obtain a result of LU decomposition i.e. L and U;

利用LU分解的结果求解线性方程求出逆矩阵，即利用S _tS _t ^-1＝I _M，设置循环变量n从1逐一增加到P，在第n次循环中，定义向量k从d(n)+1逐一增加到d(n+1)，其中d(n)和d(n+1)分别表示为向量d(n+1)中的第n个和第n+1个元素，计算中间变量矩阵Y的第k行，即

Use the result of LU decomposition to solve the linear equation to find the inverse matrix, that is, use S _t S _t ^-1 =I _M , set the loop variable n to increase from 1 to P one by one. In the nth loop, define the vector k from d(n )+1 is increased one by one to d(n+1), where d(n) and d(n+1) are respectively represented as the nth and n+1th elements in the vector d(n+1), and calculate the middle The kth row of the variable matrix Y, namely

得出所述中间变量矩阵Y的后M-D _p列，设置循环变量k从D _p+1逐一增加到M，在第k次循环中，计算所述中间变量矩阵Y的第k行，即Y(k，：)＝I(k，：)L(k，1：k-1)Y(1：k-1，：)；以及 _{The last MD p} column of the intermediate variable matrix Y is obtained, and the loop variable k is set _{to increase from D p} +1 to M one by one. In the kth loop, the kth row of the intermediate variable matrix Y is calculated, that is, Y( k,:)=I(k,:)L(k,1:k-1)Y(1:k-1,:); and

得到逆矩阵

定义循环变量k从N逐一递减到1，在第k次循环中，定义f取变量M-D _p和k+1中的较大者，求解逆矩阵

的第k行，即

Get the inverse matrix

Define the loop variable k to decrease one by one from N to 1, in the kth loop, define f to take _{the larger of the variables MD p} and k+1, and solve the inverse matrix

The kth line of

本申请实施例所述的OTFS***线性均衡装置包括：The linear equalization device of the OTFS system described in the embodiment of the present application includes:

有效信道矩阵确定模块，用于确定OTFS***在矩形窗限制条件下的时延-多普勒域的有效信道矩阵；The effective channel matrix determination module is used to determine the effective channel matrix of the OTFS system in the time delay-Doppler domain under the restriction of the rectangular window;

评估矩阵确定模块，用于根据上述有效信道矩阵确定线性均衡评估矩阵；以及The evaluation matrix determination module is used to determine the linear equalization evaluation matrix according to the above effective channel matrix; and

均衡模块，用于根据上述线性均衡评估矩阵对接收的采样信号进行均衡。The equalization module is used to equalize the received sampling signal according to the linear equalization evaluation matrix.

本申请实施例所述电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述程序时实现上述线性均衡方法。The electronic device described in the embodiment of the present application includes a memory, a processor, and a computer program that is stored on the memory and can run on the processor, and is characterized in that the above linear equalization method is implemented when the processor executes the program.

本申请实施例所述计算机可读存储介质，其上存储有计算机指令，在处理器执行上述计算机指令时实现上述线性均衡方法。The computer-readable storage medium described in the embodiment of the present application has computer instructions stored thereon, and the linear equalization method described above is implemented when the processor executes the computer instructions.

从上面所述可以看出，本发明提供的一种OTFS***线性均衡方法、装置、电子设备与计算机可读存储介质，通过对矩形窗条件下的OTFS***的信道结构进行分析，可以确定OTFS***的时延-多普勒域有效信道矩阵，进而根据上述有效信道矩阵确定线性均衡所采用的线性均衡评估矩阵，最后，再根据确定的评估矩阵进行线性均衡。本申请提供的线性均衡方式所针对的信道情景是更加贴合实际通信环境的矩形窗条件，具备实用性，并且确定线性均衡评估矩阵过程的计算复杂度与实际实施难度大大降低，因而具有较高的实用性。It can be seen from the above that the OTFS system linear equalization method, device, electronic equipment and computer-readable storage medium provided by the present invention can determine the OTFS system by analyzing the channel structure of the OTFS system under the rectangular window condition The delay-Doppler domain effective channel matrix is further determined according to the above effective channel matrix to determine the linear equalization evaluation matrix used for linear equalization, and finally, linear equalization is performed according to the determined evaluation matrix. The channel scenario for the linear equalization method provided in this application is a rectangular window condition that is more suitable for the actual communication environment, has practicality, and the calculation complexity and the actual implementation difficulty of the process of determining the linear equalization evaluation matrix are greatly reduced, so it has a high Practicality.

附图说明Description of the drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work.

图1为本发明一些实施例所述的OTFS***100的内部结构示意图；FIG. 1 is a schematic diagram of the internal structure of an OTFS system 100 according to some embodiments of the present invention;

图2为本发明一些实施例所述的OTFS***线性均衡方法示意图；2 is a schematic diagram of a linear equalization method for an OTFS system according to some embodiments of the present invention;

图3为本发明一些实施例所述的根据有效信道矩阵确定迫零均衡的评估矩阵方法示意图；3 is a schematic diagram of a method for determining an evaluation matrix of zero-forcing equalization according to an effective channel matrix according to some embodiments of the present invention;

图4为本发明一些实施例所述的根据有效信道矩阵确定最小均方差均衡的评估矩阵方法示意图；4 is a schematic diagram of an evaluation matrix method for determining minimum mean square error equalization according to an effective channel matrix according to some embodiments of the present invention;

图5为本发明实施例所提供的一种OTFS***线性均衡方法的***误码率仿真结果图；5 is a diagram of system error rate simulation results of an OTFS system linear equalization method provided by an embodiment of the present invention;

图6为本发明实施例所提供的一种OTFS***线性均衡装置结构示意图；以及6 is a schematic structural diagram of a linear equalization device for an OTFS system provided by an embodiment of the present invention; and

图7为本发明实施例所提供的一种OTFS***线性均衡电子设备示意图。FIG. 7 is a schematic diagram of an OTFS system linear equalization electronic device provided by an embodiment of the present invention.

具体实施方式detailed description

为使本发明的目的、技术方案和优点更加清楚明白，以下结合具体实施例，并参照附图，对本发明进一步详细说明。In order to make the objectives, technical solutions, and advantages of the present invention clearer, the following further describes the present invention in detail in conjunction with specific embodiments and with reference to the accompanying drawings.

需要说明的是，本发明实施例中所有使用“第一”和“第二”的表述均是为了区分两个相同名称非相同的实体或者非相同的参量，可见“第一”“第二”仅为了表述的方便，不应理解为对本发明实施例的限定，后续实施例对此不再一一说明。It should be noted that all the expressions "first" and "second" in the embodiments of the present invention are used to distinguish two entities with the same name but not the same or parameters that are not the same, as shown in "first" and "second" Only for the convenience of presentation, it should not be construed as a limitation to the embodiments of the present invention, and subsequent embodiments will not describe this one by one.

如前所述，OTFS作为一种新型多载波调制技术，能够有效对抗高动态的通信信道环境，展现出对高多普勒拓展的强鲁棒性。As mentioned earlier, OTFS, as a new type of multi-carrier modulation technology, can effectively combat the highly dynamic communication channel environment and exhibit strong robustness to high Doppler expansion.

图1为本发明一些实施例所述的OTFS***100的内部结构示意图。如图1所示，上述OTFS***100包括：OTFS发送端101和OTFS接收端102。其中，OTFS发送端101和OTFS接收端102之间经过信道103传递信号。需要说明的是，在本发明的实施例中，上述信道103可以线性时变(LTV)信道。FIG. 1 is a schematic diagram of the internal structure of an OTFS system 100 according to some embodiments of the present invention. As shown in FIG. 1, the above-mentioned OTFS system 100 includes: an OTFS sending end 101 and an OTFS receiving end 102. Wherein, the OTFS transmitting terminal 101 and the OTFS receiving terminal 102 transmit signals through the channel 103. It should be noted that, in the embodiment of the present invention, the aforementioned channel 103 may be a linear time varying (LTV) channel.

如图1所示，上述OTFS发送端101的内部可以包括：逆辛有限傅里叶变换(ISFFT)发送窗1011和OFDM调制器1012。上述OTFS接收端102的内部可以包括：OFDM解调器1021、辛有限傅里叶变换(SFFT)接收窗1022和均衡器1033。As shown in FIG. 1, the inside of the above-mentioned OTFS transmitting terminal 101 may include: an inverse symplectic finite Fourier transform (ISFFT) transmitting window 1011 and an OFDM modulator 1012. The interior of the above-mentioned OTFS receiving terminal 102 may include: an OFDM demodulator 1021, a symplectic finite Fourier transform (SFFT) receiving window 1022, and an equalizer 1033.

从图1可以看出，上述OTFS***100的模型与传统OFDM***模型类似，可将其看作是在OFDM的基础上，在发送端新增了从时延-多普勒域到时频域的转换预处理以及在接收端新增了从时频域到时延-多普勒域的转换以及信号均衡的后处理。It can be seen from Figure 1 that the model of the above-mentioned OTFS system 100 is similar to the traditional OFDM system model. It can be regarded as based on OFDM, with the addition of the delay-Doppler domain to the time-frequency domain at the transmitting end. The conversion pre-processing and the new conversion from the time-frequency domain to the delay-Doppler domain and the post-processing of signal equalization are added at the receiving end.

针对现有均衡方案实用性较低的问题，本申请的实施例提供了一种OTFS***线性均衡方法，该方法可以由OTFS***的OTFS接收端执行。In view of the problem of low practicability of the existing equalization scheme, the embodiment of the present application provides a linear equalization method of the OTFS system, which can be executed by the OTFS receiving end of the OTFS system.

图2显示了本申请实施例所述的OTFS***线性均衡方法的流程。如图2所示，上述OTFS***的线性均衡方法可以包括：Fig. 2 shows the flow of the linear equalization method of the OTFS system according to the embodiment of the present application. As shown in Fig. 2, the linear equalization method of the above-mentioned OTFS system may include:

在步骤202：确定OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵。In step 202: Determine the effective channel matrix of the OTFS system in the delay-Doppler domain under the restriction of the rectangular window.

在步骤204：根据上述有效信道矩阵确定线性均衡评估矩阵。In step 204: determine a linear equalization evaluation matrix according to the above effective channel matrix.

在步骤206：根据上述线性均衡评估矩阵对接收的采样信号进行均衡。In step 206: equalize the received sampled signal according to the linear equalization evaluation matrix.

下面就结合附图详细说明上述OTFS***线性均衡方法各个步骤的具体实现方法。长度为N×M的调制符号受多普勒效应影响，转化为时延-多普勒域调制信号x[k，l]，k＝1，2，…，N，l＝1，2，…，M。此时，如图1中所示，上述OTFS***100的OTFS发送端101中的ISFFT发送窗1011对上述时延-多普勒域调制信号x[k，l]进行ISFFT变换，并利用时域长度为N，频域长度为M的矩形窗发射函数对ISFFT变换后的所述时延-多普勒域调制信号x[k，l]进行处理，得到时间-频率域调制信号x _t-f。 The specific implementation method of each step of the above-mentioned OTFS system linear equalization method will be described in detail below with reference to the accompanying drawings. A modulation symbol with a length of N×M is affected by the Doppler effect and transformed into a time delay-Doppler domain modulation signal x[k,l], k=1,2,...,N,l=1,2,... , M. At this time, as shown in FIG. 1, the ISFFT sending window 1011 in the OTFS sending end 101 of the OTFS system 100 performs ISFFT transformation on the time delay-Doppler domain modulated signal x[k, l], and uses the time domain A rectangular window emission function with length N and frequency domain length M processes the time delay-Doppler domain modulation signal x[k, l] after ISFFT transformation to obtain a time-frequency domain modulation signal x _tf .

接下来，上述OTFS***100的OTFS发送端101中的OFDM调制器1012对上述时间-频率域调制信号x _t-f进行OFDM处理，得到时域发射信号s(t)，也即上述时间-频率域调制信号x _t-f经过OFDM调制处理被向量化调制到载波上。此后，上述时域发射信号s(t)通过线性时变的信道103后由上述OTFS***100的OTFS接收端102接收。其中，上述时域发射信号s(t)通过线性时变的信道103的过程可以表示为多径信道的信道增益和信号的卷积关系。 Next, the OFDM modulator 1012 in the OTFS transmitting end 101 of the OTFS system 100 _{performs OFDM processing on the time-frequency domain modulation signal x tf} to obtain the time-domain transmission signal s(t), that is, the aforementioned time-frequency domain modulation The signal x _tf is vectorized and modulated onto the carrier after OFDM modulation processing. After that, the time-domain transmission signal s(t) is received by the OTFS receiving end 102 of the OTFS system 100 after passing through the linear time-varying channel 103. Wherein, the above-mentioned process of the time-domain transmission signal s(t) passing through the linear time-varying channel 103 can be expressed as the convolution relationship between the channel gain of the multipath channel and the signal.

在本申请的一些实施例中，上述OTFS***100的OTFS接收端102对接收到的经过线性时变信道的时域发射信号s(t)进行采样可以得到采样后的接收信号r(k′)。其中，上述接收信号r(k′)可如下表达式(1)所示：In some embodiments of the present application, the OTFS receiving end 102 of the above-mentioned OTFS system 100 samples the received time-domain transmission signal s(t) through the linear time-varying channel to obtain the sampled received signal r(k′) . Among them, the above received signal r(k′) can be represented by the following expression (1):

其中，k′表示采样时刻；l′表示第l′条时延径，上述多径信道共由L条所述时延径组成；h(k′，l′)表示所述时变信道的脉冲响应；w(k′)表示加性高斯白噪声。Among them, k′ represents the sampling time; l′ represents the l′th delay path, and the above-mentioned multipath channel is composed of L delay paths; h(k′,l′) represents the pulse of the time-varying channel Response; w(k') represents additive white Gaussian noise.

接下来，上述OTFS***100的OTFS接收端102需要执行与上述发送端相反的操作，即对所述接收信号r(k′)进行解调。Next, the OTFS receiving end 102 of the above-mentioned OTFS system 100 needs to perform the opposite operation to the above-mentioned transmitting end, that is, demodulating the received signal r(k′).

具体地，上述OTFS***100的OTFS接收端102中的OFDM解调器1021对所述接收信号r(k′)进行OFDM解调处理，然后，SFFT接收窗1022对解调后的所述接收信号r(k′)进行SFFT变换，得到上述采样信号y[k，l]，k＝1，2，…，N，l＝1，2，…，M。Specifically, the OFDM demodulator 1021 in the OTFS receiving end 102 of the OTFS system 100 performs OFDM demodulation processing on the received signal r(k′), and then, the SFFT receiving window 1022 performs OFDM demodulation on the demodulated received signal SFFT transformation is performed on r(k′) to obtain the above-mentioned sample signal y[k,l], k=1, 2,..., N, l=1, 2,...,M.

在本申请的一些实施例中，上述采样信号y[k，l]的矩阵表示形式可由如下表达式(2)确定：In some embodiments of the present application, the matrix representation form of the sampling signal y[k,l] can be determined by the following expression (2):

其中，y为以上述采样信号y[k，l]为元素的矩阵按照行列向量化后的维度为NM×1的列向量；x为与上述时延-多普勒域调制信号x[k，l]相对应的维度为NM×1的列向量；F _N，F _M分别是N点和M点傅里叶变换矩阵；

分别是N点和M点的逆傅里叶变换矩阵；I _N表示N阶单位矩阵；

表示克罗内克乘积；V和U分别表示接收窗函数与发射窗函数，w表示噪声向量。 Among them, y is a column vector whose dimension is NM×1 after the matrix with the above-mentioned sampling signal y[k,l] as elements is vectorized according to the row and column; x is the same as the above-mentioned delay-Doppler domain modulation signal x[k, l] The corresponding dimension is the column vector of NM×1; F _N and F _M are the N-point and M-point Fourier transform matrices respectively;

Are the inverse Fourier transform matrices of N points and M points respectively; I _N represents the N-order unit matrix;

Represents the Kronecker product; V and U represent the receiving window function and the transmitting window function, respectively, and w represents the noise vector.

其中，矩阵

是一个NM×NM的块对角方阵，表示循环前缀的长度大于信道的最大时延条件下的时域信道矩阵，

表示第p个OFDM符号经过的时域信道矩阵。 Among them, the matrix

It is an NM×NM block diagonal square matrix, which means that the length of the cyclic prefix is greater than the time domain channel matrix under the condition of the maximum delay of the channel,

Represents the time-domain channel matrix through which the p-th OFDM symbol passes.

其中，所述时域信道矩阵

在循环前缀大于信道最大时延的条件下，每个OFDM符号间没有符号间干扰，所述时域信道矩阵

的结构只和信道的多径时延在时延轴上的具***置有关。 Wherein, the time domain channel matrix

Under the condition that the cyclic prefix is greater than the maximum channel delay, there is no inter-symbol interference between each OFDM symbol, and the time domain channel matrix

The structure of is only related to the specific position of the channel's multipath delay on the delay axis.

在本申请的一些可选实施例所提供的一种OTFS***线性均衡方法中，上述OTFS***100的OTFS发送端101中的OFDM调制器1012对上述时间-频率域调制信号x _t-f进行OFDM处理，得到时域发射信号s(t)具体可以包括： In an OTFS system linear equalization method provided by some optional embodiments of the present application, the OFDM modulator 1012 in the OTFS transmitting end 101 of the OTFS system 100 performs OFDM processing _{on the time-frequency domain modulated signal x tf,} Obtaining the time domain transmission signal s(t) may specifically include:

首先，对上述时间-频率域调制信号x _t-f进行逆快速傅里叶变换(Inversion Fast Fourier Transform，IFFT)将频率域信号转换为时域信号； First, perform an inverse fast Fourier transform (Inversion Fast Fourier Transform, IFFT) on the time-frequency domain modulation signal x _{tf to convert the frequency domain signal into a time domain signal;}

然后，为转换为时域信号的每个发送符号添加合适长度的循环前缀CP；Then, add a cyclic prefix CP of an appropriate length to each transmitted symbol converted into a time domain signal;

最后，通过矩形发射函数对添加循环前缀后的所述时域信号进行信号向量化处理，得到向量化调制到载波上的所述时域发射信号s(t)。Finally, signal vectorization processing is performed on the time-domain signal after adding the cyclic prefix through a rectangular transmission function to obtain the time-domain transmission signal s(t) vectorized and modulated onto the carrier.

在本申请的一些实施例中，根据上述采样信号，可以确定OTFS***在矩形窗限制条件下的时延-多普勒域的有效信道矩阵，具体可以包括：In some embodiments of the present application, according to the above-mentioned sampled signal, the effective channel matrix of the delay-Doppler domain of the OTFS system under the restriction of the rectangular window may be determined, which may specifically include:

首先，根据上述如公式(2)所述的采样信号y，能够根据如下表达式(3)确定OTFS***的时延-多普勒域的有效信道矩阵H _eff，具体为： First, according to the above-mentioned sampling signal y as described in formula (2), the effective channel matrix H _eff of the delay-Doppler domain of the OTFS system can be determined according to the following expression (3), which is specifically:

接下来，可知在矩形窗发射函数条件下，上述接收窗函数V与发射窗函数U可以满足以下条件：Next, it can be known that under the condition of the rectangular window transmitting function, the above receiving window function V and transmitting window function U can meet the following conditions:

由此，可以将上述有效信道矩阵化简为如下表达式(4)所示的在矩形窗限制条件下的时延-多普勒域的有效信道矩阵：Therefore, the above effective channel matrix can be simplified into the effective channel matrix in the delay-Doppler domain under the restriction of the rectangular window as shown in the following expression (4):

进一步，将上述有效信道矩阵H _eff表达式(4)展开表示，也即可以将上述有效信道矩阵H _eff分解为N×N个循环小矩阵

其中k″＝1，2，…，N，i″＝1，2，…，M。 Further, the above effective channel matrix H _eff expression (4) is expanded and expressed, that is, the above effective channel matrix H _eff can be decomposed into N×N small circulant matrices

Where k"=1, 2,..., N, i"=1, 2,...,M.

具体地，组成上述有效信道矩阵H _eff的循环小矩阵

可以由如下公式(5)表示： Specifically, the circulant small matrix forming the effective channel matrix H _eff

It can be expressed by the following formula (5):

其中，f _i″p是离散傅里叶变换矩阵的元素，f′ _pk″是逆离散傅里叶变换矩阵的元素。 Among them, f _i"p is an element of the discrete Fourier transform matrix, and _f'pk" is an element of the inverse discrete Fourier transform matrix.

更进一步，根据上述离散傅里叶变换矩阵的元素f _i″p与上述逆离散傅里叶变换矩阵的元素f′ _pk″对上述循环小矩阵进一步化简：也即将元素f _i″p的值与元素f′ _pk″的值代入，进行进一步简化，可以得到如下的表达式(6)： Furthermore, according to the element f _i"p of the above discrete Fourier transform matrix and the element _f'pk" of the above inverse discrete Fourier transform matrix, the circulant small matrix is further simplified: that is, the value of the _{element f i"p} Substituting the value of the element _f'pk" for further simplification, the following expression (6) can be obtained:

根据表达式(6)能够得知

只由下标之间的差值决定，而与具体的下标值无关，因此定义n＝[k″-i″] _N+1，表达式(6)可进一步简化为表达式(7)： According to expression (6), we can know

It is only determined by the difference between the subscripts, and has nothing to do with the specific subscript value. Therefore, by defining n=[k″-i″] _N +1, the expression (6) can be further simplified to the expression (7):

由此，能够确定上述有效信道矩阵H _eff为由N×N个循环小矩阵A _n组成的块循环矩阵。 Accordingly, it is possible to determine the effective channel matrix H _eff block circulant matrix by N × N matrix A _n small cycle thereof.

通过以上分析，在上述步骤202可以得到上述OTFS***在矩形窗限制条件下的时延-多普勒域的所述有效信道矩阵H _eff可以表示为如下表达式(8)所示的矩阵形式： _{Through the above analysis, in the above step 202, the effective channel matrix H eff} of the delay-Doppler domain of the above OTFS system under the restriction of the rectangular window can be obtained, which can be expressed as the matrix form shown in the following expression (8):

通过上述分析可以看出，上述有效信道矩阵H _eff为由N×N个循环小矩阵A _n组成的块循环矩阵，且其中每个循环小矩阵A _n可以根据时域信道矩阵确定。其中，每个循环小矩阵A _n与时域信道矩阵的之间的关系可以参考上述表达式(7)。 Analysis can be seen from the above, the effective channel matrix H _eff block circulant matrix by N × N matrix A _n small cycle thereof, and wherein each cycle a small matrix A _n may be determined according to the time-domain channel matrix. Wherein, the relationship between each cycle A _n submatrix of the channel matrix temporal reference may Expression (7).

具体地，在本申请的一些实施例中，在上述步骤202可以包括：Specifically, in some embodiments of the present application, the foregoing step 202 may include:

在步骤2022：根据时域信道矩阵

确定组成上述有效信道矩阵的循环小矩阵A _n。 In step 2022: According to the time domain channel matrix

Determine the small circulant matrix A _n constituting the above effective channel matrix.

具体地，对上述表达式(7)进行变形，可以得到下述表达式(9)，可以根据下述表达式(9)确定组成上述有效信道矩阵的循环小矩阵A _n，也即每个循环小矩阵A _n可以根据OFDM每个符号在时域经过的信道矩阵的傅里叶变换得出： Specifically, by modifying the above expression (7), the following expression (9) can be obtained, and the cyclic small matrix A _n constituting the effective channel matrix can be determined according to the following expression (9), that is, each cycle a _n submatrix may be a time domain through Fourier transformation of the channel matrix of each OFDM symbol is derived in accordance with:

其中，

表示所述时域信道矩阵

中第p个OFDM符号经过的时域信道矩阵。运算符FFT _Mtx()表示对一系列矩阵进行快速傅里叶变换操作，变换得到的结果也是一系列矩阵。其中，运算符FFT _Mtx()与传统傅里叶变换的最大区别是进行傅里叶变换的不是一系列数值而是一系列的矩阵，最终得到的结果也是一系列矩阵。由于傅里叶变换是线性变换，A _n的结构与

的结构保持一致。 among them,

Represents the time domain channel matrix

The time-domain channel matrix through which the p-th OFDM symbol in. The operator FFT _Mtx () represents a fast Fourier transform operation on a series of matrices, and the result of the transformation is also a series of matrices. Among them, _{the biggest difference between the operator FFT Mtx} () and the traditional Fourier transform is that the Fourier transform is not a series of values but a series of matrices, and the final result is also a series of matrices. Since the Fourier transform is a linear transform, A _n structure and

The structure remains the same.

在步骤2024：根据上述循环小矩阵A _n确定上述有效信道矩阵H _eff。 In Step 2024: the circulation of small matrix A _n is determined based on the effective channel matrix H _eff.

如前所述，在矩形窗条件下条的基于OFDM的OFTS***在时延-多普勒域有效信道矩阵是一个如表达式(8)所示的块循环矩阵，因此，可以根据上述表达式(8)确定OFTS***在矩形窗限制条件下的时延-多普勒域有效信道矩阵。As mentioned above, the effective channel matrix of the OFDM-based OFTS system in the delay-Doppler domain under the rectangular window condition is a block circulant matrix as shown in expression (8). Therefore, it can be based on the above expression (8) Determine the effective channel matrix of the delay-Doppler domain of the OFTS system under the restriction of the rectangular window.

在本申请的一些实施例中，在上述步骤204，可以根据上述有效信道矩阵确定线性均衡评估矩阵。In some embodiments of the present application, in the foregoing step 204, a linear equalization evaluation matrix may be determined according to the foregoing effective channel matrix.

在本申请的一些实施例中，上述OTFS接收端可以采用迫零均衡方法，此时，根据上述有效信道矩阵可以确定迫零均衡评估矩阵。In some embodiments of the present application, the above-mentioned OTFS receiving end may adopt a zero-forcing equalization method. In this case, the zero-forcing equalization evaluation matrix can be determined according to the above-mentioned effective channel matrix.

具体地，根据上述有效信道矩阵可以对在时延-多普勒域的迫零均衡进行简化，其中，上述迫零均衡评估矩阵可以由如下表达式(10)表示：Specifically, the zero-forcing equalization in the time delay-Doppler domain can be simplified according to the above-mentioned effective channel matrix, where the above-mentioned zero-forcing equalization evaluation matrix can be expressed by the following expression (10):

W _ZF＝H _eff ^-1 (10) W _ZF ＝H _eff ^-1 (10)

即对所述有效信道矩阵H _eff求逆可得到所述评估矩阵W _ZF。由于上述有效信道矩阵H _eff是块循环矩阵，对其求逆后所得矩阵也是块循环矩阵，由此，上述评估矩阵W _ZF可以由如下表达式(11)表示： That is, the effective channel matrix H _{eff is} inverted to obtain the evaluation matrix W _ZF . Since the above effective channel matrix H _eff is a block circulant matrix, and the matrix obtained after its inversion is also a block circulant matrix, the above evaluation matrix W _ZF can be expressed by the following expression (11):

W _ZF＝H _eff ^-1＝circ{B ₁，B ₂，…，B _N} (11) W _ZF ＝H _eff ^-1 ＝circ{B ₁ , B ₂ ,..., B _N } (11)

进一步，根据上述有效信道矩阵与时域信道的关系，能够确定所述评估矩阵W _ZF的循环小矩阵B _q与所述有效信道矩阵H _eff的循环小矩阵A _n间的计算关系，如下表达式(12)和(13)所示： Further, the relationship of the effective channel matrix and the time-domain channel, it is possible to determine the evaluation calculating the relationship between the matrix W _ZF cyclic submatrix B _q of the effective channel matrix H _eff cyclic submatrix A _n, the following expression (12) and (13) show:

其中，B _q，

Among them, B _q ,

随后，将上述表达式(9)代入上述表达式(13)，及可以求得上述中间矩阵S _t。 Subsequently, the above-mentioned expression (9) is substituted into the above-mentioned expression (13), and the above-mentioned intermediate matrix S _t can be obtained.

进一步，对上述中间矩阵S _t求逆，根据求逆结果确定所述评估矩阵W _ZF的循环小矩阵B _q，最后得到所述评估矩阵W _ZF。 Further, the above intermediate matrix S _t inversion, determining the evaluation matrix W _ZF cyclic submatrix B _q The inversion result, the finally obtained evaluation matrix W _ZF.

通过上述分析可以看出，在采用迫零均衡方式时，上述OTFS接收端可以通过如下方法根据上述有效信道矩阵确定迫零均衡的评估矩阵。具体实现过程可以如图3所示，包括：It can be seen from the above analysis that when the zero-forcing equalization mode is adopted, the above-mentioned OTFS receiving end can determine the evaluation matrix of the zero-forcing equalization according to the above effective channel matrix by the following method. The specific implementation process can be shown in Figure 3, including:

在步骤302：对上述循环小矩阵A _n进行逆快速傅里叶变换得到中间矩阵S _t； In step 302: perform inverse fast Fourier transform on the small circulant matrix A _n to obtain an intermediate matrix S _t ;

在步骤304：对上述中间矩阵S _t求逆； In Step 304: the above intermediate matrix S _t inversion;

在步骤306：对上述求逆后的中间矩阵S _t ^-1进行快速傅里叶变换得到迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q；以及 In step 306: Fast Fourier transform is performed on the intermediate matrix S _t ^-1 after the above inversion to obtain the second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF ; and

在步骤308：根据迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q确定迫零均衡评估矩阵W _ZF。 In step 308: Determine the zero-forcing equalization evaluation matrix W _ZF according to the second circulant small matrix B _q of the zero-forcing equalization evaluation matrix W _ZF .

在确定了迫零均衡评估矩阵W _ZF之后，在步骤206，上述OTFS接收端可以进一步直接根据确定的上述迫零均衡评估矩阵W _ZF对接收的采样信号进行均衡，从而得到接收的估计信号。 After the zero-forcing equalization evaluation matrix W _{ZF is} determined, in step 206, the above-mentioned OTFS receiving end may further directly equalize _{the received sampling signal according to the determined zero-forcing equalization evaluation matrix W ZF} , so as to obtain the received estimated signal.

在上述OTFS***的线性均衡方法中，上述OTFS接收端可以根据有效信道和时域信道的关系确定有效信道矩阵的特征，并根据上述有效信道矩阵的特征对时延-多普勒域的迫零均衡评估矩阵进行简化，得到低复杂度的确定迫零均衡评估矩阵的方法。本领域的技术人员可以理解，传统的迫零均衡计算复杂度为

而在本申请的实施例中，上述迫零均衡的复杂度为

其中D _P是信道的最大时延多径在时延-多普勒域平面时延轴上的坐标值。由此可以看出，上述OTFS***线性均衡方法的计算复杂度要远低于传统迫零均衡方法的计算复杂度，实施难度也大大降低，具有较高的实用性。 In the linear equalization method of the OTFS system, the OTFS receiver can determine the characteristics of the effective channel matrix according to the relationship between the effective channel and the time domain channel, and perform zero-forcing in the time delay-Doppler domain according to the characteristics of the effective channel matrix. The equalization evaluation matrix is simplified, and a low-complexity method for determining the zero-forcing equalization evaluation matrix is obtained. Those skilled in the art can understand that the computational complexity of traditional zero-forcing equalization is

In the embodiment of the present application, the complexity of the above zero-forcing equalization is

Where D _P is the coordinate value of the maximum delay multipath of the channel on the delay axis of the delay-Doppler domain plane. It can be seen that the calculation complexity of the linear equalization method of the above OTFS system is much lower than that of the traditional zero-forcing equalization method, the implementation difficulty is also greatly reduced, and it has high practicability.

在本申请的一些实施例中，上述OTFS接收端可以采用最小均方差均衡方法。此时，根据上述有效信道矩阵可以确定最小均方差均衡评估矩阵。In some embodiments of the present application, the above-mentioned OTFS receiving end may adopt a minimum mean square error equalization method. At this time, the minimum mean square error equalization evaluation matrix can be determined according to the above effective channel matrix.

具体的，根据上述有效信道矩阵，能够对在时延-多普勒域的最小均方差均衡进行简化，所述最小均方差均衡评估矩阵可以由如下表达式(14)表示：Specifically, according to the above effective channel matrix, the minimum mean square error equalization in the delay-Doppler domain can be simplified, and the minimum mean square error equalization evaluation matrix can be expressed by the following expression (14):

其中，

表示H _eff的共轭转置矩阵，σ ²表示信道噪声的方差，I表示相应维度的单位矩阵。 among them,

Represents the conjugate transposed matrix of _Heff ^{, σ 2} represents the variance of channel noise, and I represents the identity matrix of the corresponding dimension.

根据有效信道矩阵中的循环小矩阵A _n，可以将

展开表示为如下表达式(15)，其中，可以将

称为第二中间矩阵： According to the small circulant matrix A _{n in the effective channel matrix, the}

The expansion is expressed as the following expression (15), where, you can

Called the second intermediate matrix:

其中，[·] _N为取模操作，[N] _N＝N。 Among them, [·] _N is the modulo operation, and [N] _N =N.

由此，上述表达式(15)所示的第二中间矩阵求逆，得到

可以表示为如下表达式(16)： Thus, the second intermediate matrix shown in the above expression (15) is inverted to obtain

It can be expressed as the following expression (16):

进一步，将上述表达式(16)所示的逆矩阵与

相乘，可以得到如下表达式(17)所示的最小均方差均衡评估矩阵： Further, the inverse matrix shown in the above expression (16) and

By multiplying, the minimum mean square error equilibrium evaluation matrix shown in the following expression (17) can be obtained:

通过上述分析可以看出，在采用最小均方差均衡方式时，上述OTFS接收端可以通过如下方法根据上述有效信道矩阵确定最小均方差均衡的评估矩阵W _MMSE。具体实现过程可以如图4所示，包括： It can be seen from the above analysis that when the minimum mean square error equalization method is adopted, the above-mentioned OTFS receiving end can determine the minimum mean square error equalization evaluation matrix W _MMSE according to the above effective channel matrix by the following method. The specific implementation process can be shown in Figure 4, including:

在步骤402：根据有效信道矩阵及其转置以及信道噪声的方差，确定第二中间矩阵；In step 402: determine a second intermediate matrix according to the effective channel matrix and its transposition and the variance of the channel noise;

在步骤404：对上述第二中间矩阵求逆；In step 404: Invert the above-mentioned second intermediate matrix;

在步骤406：对上述求逆后的第二中间矩阵与有效信道矩阵的转置矩阵相乘得到最小均方差均衡评估矩阵W _MMSE。 In step 406: multiply the inverted second intermediate matrix and the transposed matrix of the effective channel matrix to obtain the minimum mean square error equalization evaluation matrix W _MMSE .

在确定了最小均方差均衡评估矩阵W _MMSE之后，在步骤206，上述OTFS接收端可以进一步根据上述最小均方差均衡评估矩阵W _MMSE对接收的采样信号进行均衡，从而得到接收的估计信号。 After determining the minimum mean square error equalization evaluation matrix W _MMSE , in step 206, the above-mentioned OTFS receiving end may further equalize _{the received sampling signal according to the above minimum mean square error equalization evaluation matrix W MMSE} to obtain the received estimated signal.

在上述OTFS***的线性均衡方法中，上述OTFS接收端可以根据有效信道和时域信道的关系确定有效信道矩阵的特征，并根据上述有效信道矩阵的特征对时延-多普勒域的迫零均衡评估矩阵进行简化，得到低复杂度的确定迫零均衡评估矩阵的方法。本领域的技术人员可以理解，传统的最小均方差均衡计算复杂度为

而在本申请的实施例中，上述最小均方差均衡方法的复杂度为

由此可以看出，上述OTFS***线性均衡方法的计算复杂度要远低于传统最小均方差均衡方法的计算复杂度，实施难度也大大降低，具有较高的实用性。 In the linear equalization method of the OTFS system, the OTFS receiver can determine the characteristics of the effective channel matrix according to the relationship between the effective channel and the time domain channel, and perform zero-forcing in the time delay-Doppler domain according to the characteristics of the effective channel matrix. The equalization evaluation matrix is simplified, and a low-complexity method for determining the zero-forcing equalization evaluation matrix is obtained. Those skilled in the art can understand that the traditional minimum mean square error equalization calculation complexity is

In the embodiment of the present application, the complexity of the above-mentioned minimum mean square error equalization method is

It can be seen that the computational complexity of the linear equalization method of the above OTFS system is much lower than that of the traditional minimum mean square error equalization method, and the difficulty of implementation is greatly reduced, which has high practicability.

在本申请的实施例中，还可以进一步对上述步骤304和404中的矩阵求逆操作进行进一步的简化。In the embodiment of the present application, the matrix inversion operations in

steps

304 and 404 can be further simplified.

以对上述步骤304中的中间矩阵S _t求逆为例，上述求逆操作可以包括： Intermediate step 304 in the above-described inverse matrix S _t as an example, the aforementioned inversion operation may include:

对运算辅助参量进行初始化定义，定义L矩阵与U矩阵分别为L＝I _M，U＝0 _M，定义中间变量矩阵Y＝0 _M，将信道的多径时延表示为向量d _chan＝[D ₁，D ₂，D ₃，…，D _P]，其中P表示多径的数量，D ₁，D ₂，D ₃，…，D _P是在多径时延在时延-多普勒平面上时延轴上的坐标值，根据实际的时延值和时延轴的分辨率参数可得，都是整数并且满足D ₁＝0，定义辅助向量d＝[d _chan，M-D _P]。 Initialize the definition of the auxiliary parameters of the operation, define the L matrix and the U matrix as L = I _M , U = 0 _M , define the intermediate variable matrix Y = 0 _M , and express the multipath delay of the channel as a vector d _chan =[D ₁ , D ₂ , D ₃ ,..., D _P ], where P represents the number of multipaths, D ₁ , D ₂ , D ₃ ,..., D _P is the multipath delay on the delay-Doppler plane The coordinate value on the delay axis can be obtained according to the actual delay value and the resolution parameter of the delay axis. They are all integers and satisfy D ₁ =0. Define the auxiliary vector d=[d _chan , MD _P ].

求解L矩阵的前M-D _P列：L(i+D _P，i)＝S _t(i+D _P，i)/S _t(i，i)。其中，L(i+D _P，i)表示L矩阵中的i+D _P行i列位置上的元素，i为循环变量，i＝1：M-D _P。 Solve the first MD _P column of the L matrix: L(i+D _P ,i)=S _t (i+D _P ,i)/S _t (i,i). Among them, L(i+D _P , i) represents _{the element at the row i column position of i+D P} in the L matrix, i is a loop variable, i=1: MD _P.

L矩阵中的前M-D _P列每列只有P个值，设置循环变量i从1逐一增加到M-D _p，在第i次循环中计算中，计算L矩阵的第i列中的P个值，用坐标形式可表示为L(i+D _P，i)＝S _t(i+D _P，i)/S _t(i，i)。 _{The first MD P} column in the L matrix has only P values in each column. Set the loop variable i to increase from 1 to MD _p one by one. In the i-th loop calculation, calculate the P values in the i-th column of the L matrix, use The coordinate form can be expressed as L(i+D _P ,i)=S _t (i+D _P ,i)/S _t (i,i).

求解U矩阵的前M-D _P行：

其中，U(ξ，；)和S _t(ξ，：)分别表示U矩阵和S _t矩阵的第ξ行，向量ξ从D _p+1逐一增加到D _p+1，其中，p为循环变量，p＝1：P+1。 Solve the first MD _P rows of the U matrix:

Wherein, U (ξ ,;) and S _t (ξ, :) line [xi] U respectively denote matrix and the matrix S _t, is increased by one from vector [xi] D _{_p} +1 D _p _{+ 1,} where, p is the loop variable , P=1: P+1.

设置循环变量p从1逐一增加到P+1，在每次循环内：计算U矩阵的第D _p+1行到第D _p+1行，定义一个向量ξ从D _p+1逐一增加到D _p+1，则U矩阵的第ξ行用坐标形式可以表示为

Set the loop variable p to increase from 1 to P+1 one by one. In each loop: calculate the D _p +1 row to D _p+1 row of the U matrix, and define a vector ξ _{to increase from D p+1} to D one by one _p+1 , then the ξth row of the U matrix can be expressed in coordinate form as

求解L矩阵的后D _P列和U矩阵的后D _P行，利用通用的LU分解方法求解，最后得到矩阵S _t的LU分解结果即L和U。 Solving the matrix L D D _P after _P of columns of the matrix U and the rows, using a common method for solving LU decomposition, LU decomposition to give the final result, i.e., the matrix S _t L and U.

得出所述中间变量矩阵Y的后M-D _p列，设置循环变量k从D _p+1逐一增加到M，在第k次循环中，计算所述中间变量矩阵Y的第k行，即Y(k，：)＝I(k，：)L(k，1：k-1)Y(1：k-1，：)。 _{The last MD p} column of the intermediate variable matrix Y is obtained, and the loop variable k is set _{to increase from D p} +1 to M one by one. In the kth loop, the kth row of the intermediate variable matrix Y is calculated, that is, Y( k,:)=I(k,:)L(k,1:k-1)Y(1:k-1,:).

得到逆矩阵

的第k行，即

由此确定所述矩阵S _t的逆矩阵

Get the inverse matrix

The kth line of

From this determine the inverse matrix of _{the matrix S t}

所述OTFS***线性均衡方法中，在根据有效信道矩阵的特征以及有效信道和时域信道的关系，对时延-多普勒域的迫零均衡方法进行简化时，采用了一种避免对全规模矩阵求逆的低复杂度求逆方法，大大降低了计算复杂度。In the linear equalization method of the OTFS system, when simplifying the zero-forcing equalization method in the delay-Doppler domain according to the characteristics of the effective channel matrix and the relationship between the effective channel and the time domain channel, a method is adopted to avoid the total compensation. The low-complexity inversion method of scale matrix inversion greatly reduces the computational complexity.

在根据有效信道矩阵的特征以及有效信道和时域信道的关系，对时延-多普勒域的最小均方差均衡方法进行简化的过程中，在对上述第二中间矩阵

求逆的过程中采用与上述中间矩阵S _t求逆方法相同的思路，同样避免对全规模矩阵求逆，能够大大降低计算复杂度。 In the process of simplifying the minimum mean square error equalization method in the delay-Doppler domain according to the characteristics of the effective channel matrix and the relationship between the effective channel and the time domain channel, the above-mentioned second intermediate matrix

Inverse process employed in the above-mentioned intermediate matrix S _t inversion same method of thinking, the same full-scale to avoid inverting the matrix can greatly reduce computational complexity.

如图5所示，是包括本发明实施例所提供的一种OTFS***线性均衡方法的***误码率仿真结果图。其中，同时还显示了现有均衡方法***误码率仿真结果。所述OTFS***线性均衡方法中的低复杂度迫零均衡方法与传统迫零均衡方法的仿真结果基本相同，所述OTFS***线性均衡方法中的低复杂度最小均方差均衡方法与传统最小均方差均衡方法的仿真结果基本相同。As shown in FIG. 5, it is a diagram of system error rate simulation results including an OTFS system linear equalization method provided by an embodiment of the present invention. Among them, the simulation result of the system error rate of the existing equalization method is also shown. The simulation results of the low-complexity zero-forcing equalization method in the OTFS system linear equalization method are basically the same as the traditional zero-forcing equalization method, and the low-complexity minimum mean square error equalization method in the OTFS system linear equalization method is the same as the traditional minimum mean square error The simulation results of the equalization method are basically the same.

在另一方面，本申请还提供了一种OTFS***线性均衡装置。图6显示了本申请的一些实施例提出的OTFS***线性均衡装置的内部结构。In another aspect, this application also provides a linear equalization device for the OTFS system. FIG. 6 shows the internal structure of the linear equalization device of the OTFS system proposed by some embodiments of the present application.

如图6所示，上述OTFS***线性均衡装置可以包括：As shown in FIG. 6, the linear equalization device of the OTFS system may include:

有效信道矩阵确定模块602，用于确定OTFS***在矩形窗限制条件下的时延-多普勒域的有效信道矩阵；The effective channel matrix determination module 602 is used to determine the effective channel matrix of the delay-Doppler domain of the OTFS system under the restriction of the rectangular window;

评估矩阵确定模块604，用于根据上述有效信道矩阵确定线性均衡评估矩阵；The evaluation matrix determination module 604 is configured to determine a linear equalization evaluation matrix according to the above effective channel matrix;

均衡模块606，用于根据上述线性均衡评估矩阵对接收的采样信号进行均衡。The equalization module 606 is configured to equalize the received sampling signal according to the linear equalization evaluation matrix.

在本申请的一些实施例中，上述有效信道矩阵确定模块602、评估矩阵确定模块 604、以及均衡模块606可以采用上述图2至图4所述的方法实现。In some embodiments of the present application, the above-mentioned effective channel matrix determination module 602, evaluation matrix determination module 604, and equalization module 606 may be implemented using the methods described in FIGS. 2 to 4 above.

在又一方面，本申请还提供了一种执行上述OTFS***线性均衡方法的电子设备。图7显示了本申请的一些实施例提出的电子设备的内部结构。In yet another aspect, the present application also provides an electronic device that executes the linear equalization method of the OTFS system. Fig. 7 shows the internal structure of the electronic device proposed in some embodiments of the present application.

如图7所示，上述电子设备可以包括：一个或多个处理器701以及存储器702。图7中以一个处理器701为例。As shown in FIG. 7, the foregoing electronic device may include: one or more processors 701 and a memory 702. In FIG. 7, a processor 701 is taken as an example.

上述执行所述OTFS***线性均衡方法的电子设备还可以包括：输入装置703和输出装置704。The above electronic device for executing the linear equalization method of the OTFS system may further include: an input device 703 and an output device 704.

处理器701、存储器702、输入装置703和输出装置704可以通过总线或者其他方式连接，图7中以通过总线连接为例。The processor 701, the memory 702, the input device 703, and the output device 704 may be connected by a bus or in other ways. In FIG. 7, the connection by a bus is taken as an example.

存储器702作为一种非易失性计算机可读存储介质，可用于存储非易失性软件程序、非易失性计算机可执行程序以及模块，如本申请实施例中的所述OTFS***线性均衡方法对应的程序指令/模块。处理器701通过运行存储在存储器702中的非易失性软件程序、指令以及模块，从而执行服务器的各种功能应用以及数据处理，即实现上述方法实施例的OTFS***线性均衡方法。The memory 702, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs and modules, as described in the OTFS system linear equalization method in the embodiment of the present application Corresponding program instructions/modules. The processor 701 executes various functional applications and data processing of the server by running non-volatile software programs, instructions, and modules stored in the memory 702, that is, realizing the linear equalization method of the OTFS system in the foregoing method embodiment.

存储器702可以包括存储程序区和存储数据区，其中，存储程序区可存储操作***、至少一个功能所需要的应用程序；存储数据区可存储根据执行所述OTFS***线性均衡方法的装置的使用所创建的数据等。此外，存储器702可以包括高速随机存取存储器，还可以包括非易失性存储器，例如至少一个磁盘存储器件、闪存器件、或其他非易失性固态存储器件。在一些实施例中，存储器702可选包括相对于处理器701远程设置的存储器，这些远程存储器可以通过网络连接至会员用户行为监控装置。上述网络的实例包括但不限于互联网、企业内部网、局域网、移动通信网及其组合。The memory 702 may include a storage program area and a storage data area. The storage program area may store an operating system and an application program required by at least one function; Created data, etc. In addition, the memory 702 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the memory 702 may optionally include a memory remotely provided with respect to the processor 701, and these remote memories may be connected to a member user behavior monitoring device through a network. Examples of the aforementioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

输入装置703可接收输入的数字或字符信息，以及产生与执行所述OTFS***线性均衡方法装置的用户设置以及功能控制有关的键信号输入。输出装置704可包括显示屏等显示设备。The input device 703 can receive inputted digital or character information, and generate key signal inputs related to user settings and function control of the device for performing the linear equalization method of the OTFS system. The output device 704 may include a display device such as a display screen.

所述一个或者多个模块存储在所述存储器702中，当被所述一个或者多个处理器701执行时，执行上述任意方法实施例中的OTFS***线性均衡方法。所述执行所述OTFS***线性均衡方法的装置的实施例，其技术效果与前述任意方法实施例相同或者类似。The one or more modules are stored in the memory 702, and when executed by the one or more processors 701, the OTFS system linear equalization method in any of the foregoing method embodiments is executed. The technical effect of the embodiment of the apparatus for executing the linear equalization method of the OTFS system is the same as or similar to any of the foregoing method embodiments.

上述实施例的装置用于实现前述实施例中相应的方法，并且具有相应的方法实施例的有益效果，在此不再赘述。The device in the foregoing embodiment is used to implement the corresponding method in the foregoing embodiment, and has the beneficial effects of the corresponding method embodiment, which will not be repeated here.

所属领域的普通技术人员应当理解：以上任何实施例的讨论仅为示例性的，并非旨在暗示本公开的范围(包括权利要求)被限于这些例子；在本发明的思路下，以上实施例或者不同实施例中的技术特征之间也可以进行组合，步骤可以以任意顺序实现，并存在如上所述的本发明的不同方面的许多其它变化，为了简明它们没有在细节中提供。Those of ordinary skill in the art should understand that the discussion of any of the above embodiments is only exemplary, and is not intended to imply that the scope of the present disclosure (including the claims) is limited to these examples; under the idea of the present invention, the above embodiments or The technical features in the different embodiments can also be combined, the steps can be implemented in any order, and there are many other changes in the different aspects of the present invention as described above, which are not provided in the details for the sake of brevity.

另外，为简化说明和讨论，并且为了不会使本发明难以理解，在所提供的附图中可以示出或可以不示出与集成电路(IC)芯片和其它部件的公知的电源/接地连接。此外，可以以框图的形式示出装置，以便避免使本发明难以理解，并且这也考虑了以下事实，即关于这些框图装置的实施方式的细节是高度取决于将要实施本发明的平台的(即，这些细节应当完全处于本领域技术人员的理解范围内)。在阐述了具体细节(例如，电路)以描述本发明的示例性实施例的情况下，对本领域技术人员来说显而易见的是，可以在没有这些具体细节的情况下或者这些具体细节有变化的情况下实施本发明。因此，这些描述应被认为是说明性的而不是限制性的。In addition, in order to simplify the description and discussion, and in order not to obscure the present invention, the well-known power/ground connections to integrated circuit (IC) chips and other components may or may not be shown in the drawings provided. . In addition, the devices may be shown in the form of block diagrams in order to avoid making the present invention difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform on which the present invention will be implemented (ie , These details should be completely within the understanding of those skilled in the art). In the case where specific details (for example, circuits) are described to describe exemplary embodiments of the present invention, it is obvious to those skilled in the art that it may be possible without these specific details or when these specific details are changed. The present invention is implemented below. Therefore, these descriptions should be considered illustrative rather than restrictive.

尽管已经结合了本发明的具体实施例对本发明进行了描述，但是根据前面的描述，这些实施例的很多替换、修改和变型对本领域普通技术人员来说将是显而易见的。例如，其它存储器架构(例如，动态RAM(DRAM))可以使用所讨论的实施例。Although the present invention has been described in conjunction with specific embodiments of the present invention, many substitutions, modifications and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may use the discussed embodiments.

本发明的实施例旨在涵盖落入所附权利要求的宽泛范围之内的所有这样的替换、修改和变型。因此，凡在本发明的精神和原则之内，所做的任何省略、修改、等同替换、改进等，均应包含在本发明的保护范围之内。The embodiments of the present invention are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

一种正交时频空OTFS***线性均衡方法，其特征在于，包括：A linear equalization method for an orthogonal time-frequency space OTFS system, which is characterized in that it includes:

确定所述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵；Determining the effective channel matrix of the OTFS system in the delay-Doppler domain under the restriction of the rectangular window;

根据所述有效信道矩阵确定线性均衡评估矩阵；以及Determining a linear equalization evaluation matrix according to the effective channel matrix; and

根据上述线性均衡评估矩阵对接收的采样信号进行均衡。The received sampling signal is equalized according to the above linear equalization evaluation matrix.
根据权利要求1所述的方法，其特征在于，所述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵H _eff为由N×N个循环小矩阵A _n组成的块循环矩阵，其中，循环小矩阵A _n根据时域信道矩阵确定；以及 The method according to claim 1, wherein said system OTFS rectangular window delay constraints - the block matrix H _eff by N × N matrix A _n cycles consisting of a small effective channel Doppler domain circulant matrix, wherein the matrix A _n small loop is determined according to the time-domain channel matrix; and

所述确定所述OTFS***在矩形窗限制条件下时延-多普勒域的有效信道矩阵包括：根据时域信道矩阵
确定组成上述有效信道矩阵的循环小矩阵A _n；以及根据所述循环小矩阵A _n确定所述有效信道矩阵H _eff。 The determining the effective channel matrix of the delay-Doppler domain of the OTFS system under the restriction of the rectangular window includes: according to the time domain channel matrix
Determining the composition of the effective channel matrix of small cyclic matrix A _n; and determining the effective channel matrix H _eff according to the cyclic submatrix A _n.
根据权利要求2所述的方法，其特征在于，所述根据时域信道矩阵
确定组成上述有效信道矩阵的循环小矩阵A _n包括： The method according to claim 2, characterized in that, according to the time-domain channel matrix
Determining the composition of the effective channel matrix A _n cyclic submatrix comprising:

根据如下表达式确定所述循环小矩阵A _n： _{The small circulant matrix A n is} determined according to the following expression:

其中，
表示所述时域信道矩阵
中第p个正交频分复用符号经过的时域信道矩阵；矩阵
是一个NM×NM的块对角方阵，表示循环前缀的长度大于信道的最大时延条件下的时域信道矩阵；以及运算符FFT _Mtx()表示对一系列矩阵进行快速傅里叶变换操作，变换得到的结果也是一系列矩阵。 among them,
Represents the time domain channel matrix
The matrix of the time domain channel through which the p-th orthogonal frequency division multiplexing symbol in
It is an NM×NM block diagonal square matrix, which means that the length of the cyclic prefix is greater than the time domain channel matrix under the maximum delay of the channel; and the operator FFT _Mtx () means fast Fourier transform operation on a series of matrices , The result of the transformation is also a series of matrices.
根据权利要求2所述的方法，其特征在于，所述根据所述循环小矩阵A _n确定所述有效信道矩阵H _eff包括： The method according to claim 2, wherein the determining the effective channel matrix H _eff comprising the said cyclic submatrix A _n:

根据如下表达式确定所述有效信道矩阵H _eff： _{The effective channel matrix H eff is} determined according to the following expression:
根据权利要求2所述的方法，其特征在于，所述线性均衡评估矩阵包括：迫零均衡评估矩阵W _ZF；其中， The method according to claim 2, wherein the linear equalization evaluation matrix comprises: a zero-forcing equalization evaluation matrix W _ZF ; wherein,

所述根据所述有效信道矩阵确定线性均衡评估矩阵包括：The determining a linear equalization evaluation matrix according to the effective channel matrix includes:

对所述循环小矩阵A _n进行逆快速傅里叶变换得到中间矩阵S _t； Perform an inverse fast Fourier transform on the small circulant matrix A _n _{to obtain an intermediate matrix S t} ;

对所述中间矩阵S _t求逆； The inverse intermediate matrix S _t;

对求逆后的中间矩阵S _t ^-1进行快速傅里叶变换得到迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q；以及 Fast Fourier transform is performed on the inverted intermediate matrix S _t ^-1 to obtain the second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF ; and

根据迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q确定迫零均衡评估矩阵W _ZF。 The zero-forcing equalization evaluation matrix W _ZF is determined according to the second circulant small matrix B _q of the zero-forcing equalization evaluation matrix W _ZF .
根据权利要求5所述的方法，其特征在于，所述对求逆后的中间矩阵S _t ^-1进行快速傅里叶变换得到迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q包括： The method according to claim 5, wherein the _{fast Fourier transform of the inverted intermediate matrix S t} ^-1 to obtain the second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF comprises:

根据如下表达式，确定所述迫零均衡评估矩阵W _ZF的第二循环小矩阵B _q： Determine the second circulant small matrix B _{q of the} zero-forcing equalization evaluation matrix W _ZF according to the following expression:

其中，B _q，
Among them, B _q ,
根据权利要求2所述的方法，其特征在于，所述线性均衡评估矩阵包括：最小均方差均衡的评估矩阵W _MMSE；其中， The method according to claim 2, wherein the linear equalization evaluation matrix comprises: a minimum mean square error equalization evaluation matrix W _MMSE ; wherein,

所述根据所述有效信道矩阵确定线性均衡评估矩阵包括：The determining a linear equalization evaluation matrix according to the effective channel matrix includes:

根据所述有效信道矩阵及其转置以及信道噪声的方差，确定第二中间矩阵；Determine a second intermediate matrix according to the effective channel matrix and its transposition and the variance of the channel noise;

对所述第二中间矩阵求逆；Invert the second intermediate matrix;

对所述求逆后的第二中间矩阵与有效信道矩阵的转置矩阵相乘得到最小均方差均衡评估矩阵W _MMSE。 Multiplying the inverted second intermediate matrix and the transposed matrix of the effective channel matrix to obtain the minimum mean square error equalization evaluation matrix W _MMSE .
根据权利要求7所述的方法，其特征在于，所述确定第二中间矩阵包括：根据如下表达式确定所述第二中间矩阵：The method according to claim 7, wherein the determining the second intermediate matrix comprises: determining the second intermediate matrix according to the following expression:

其中，[·] _N为取模操作，[N] _N＝N； Among them, [·] _N is the modulo operation, [N] _N ＝N;

所述对所述第二中间矩阵求逆包括：根据如下表达式对所述第二中间矩阵求逆：The inverting the second intermediate matrix includes: inverting the second intermediate matrix according to the following expression:

对所述求逆后的第二中间矩阵与有效信道矩阵的转置矩阵相乘得到最小均方差均衡评估矩阵W _MMSE包括：根据如下表达式确定所述最小均方差均衡评估矩阵W _MMSE： Multiplying the inverted second intermediate matrix and the transposed matrix of the effective channel matrix to obtain the minimum mean square error equalization evaluation matrix W _MMSE includes: determining the minimum mean square error equalization evaluation matrix W _MMSE according to the following expression:
根据权利要求5或7所述的方法，其特征在于，设所述中间矩阵或所述第二中间矩阵为S _t；所述对所述中间矩阵求逆或所述对所述第二中间矩阵求逆包括： The method according to claim 5 or 7, characterized in that, let the intermediate matrix or the second intermediate matrix be _St ; the inverse of the intermediate matrix or the pair of the second intermediate matrix Reversal includes:

对运算辅助参量进行初始化定义，定义L矩阵与U矩阵分别为L＝I _M，U＝0 _M，定义中间变量矩阵Y＝0 _M，将信道的多径时延表示为向量d _chan＝[D ₁,D ₂,D ₃,…,D _P]，其中P表示多径的数量，D ₁,D ₂,D ₃,…,D _P是在多径时延在时延-多普勒平面上时延轴上的坐标值，定义辅助向量d＝[d _chan,M-D _P]； Initialize the definition of the auxiliary parameters of the operation, define the L matrix and the U matrix as L = I _M , U = 0 _M , define the intermediate variable matrix Y = 0 _M , and express the channel multipath delay as a vector d _chan =[D ₁ ,D ₂ ,D ₃ ,…,D _P ], where P represents the number of multipaths, D ₁ ,D ₂ ,D ₃ ,…,D _P is the multipath delay on the delay-Doppler plane The coordinate value on the time delay axis defines the auxiliary vector d=[d _chan ,MD _P ];

求解L矩阵的前M-D _P列：L(i+D _P,i)＝S _t(i+D _P,i)/S _t(i,i)；其中，L(i+D _P,i)表示L矩阵中的i+D _P行i列位置上的元素，i为循环变量，i＝1：M-D _P； Solve the first MD _P column of the L matrix: L(i+D _P ,i)=S _t (i+D _P ,i)/S _t (i,i); where L(i+D _P ,i) means The element at the row i column position of i+D _P in the L matrix, i is the loop variable, i=1: MD _P ;

求解U矩阵的前M-D _P行：
其中，U(ξ,:)和S _t(ξ,:)分别表示U矩阵和S _t矩阵的第ξ行，向量ξ从D _p+1逐一增加到D _p+1，其中，p为循环变量，p＝1：P+1； Solve the first MD _P rows of the U matrix:
Among them, U(ξ,:) and _St (ξ,:) represent the ξth row of _{U matrix and St} _{matrix respectively, the vector ξ increases from D p} +1 to D _p+1 one by one, where p is the cyclic variable , P=1: P+1;

求解L矩阵的后D _P列和U矩阵的后D _P行，利用通用的LU分解方法求解，最后得到矩阵S _t的LU分解结果即L和U； After solving the row D _P D _P L columns of the matrix and the U matrix, LU decomposition using a general method to solve the last matrix S _t to obtain a result of LU decomposition i.e. L and U;

利用LU分解的结果求解线性方程求出逆矩阵，即利用S _tS _t ^-1＝I _M，设置循环变量n从1逐一增加到P，在第n次循环中，定义向量k从d(n)+1逐一增加到d(n+1)，其中d(n)和d(n+1)分别表示为向量d(n+1)中的第n个和第n+1个元素，计算中间变量矩阵Y的第k行，即
Use the result of LU decomposition to solve the linear equation to find the inverse matrix, that is, use S _t S _t ^-1 =I _M , set the loop variable n to increase from 1 to P one by one. In the nth loop, define the vector k from d(n )+1 is increased one by one to d(n+1), where d(n) and d(n+1) are respectively represented as the nth and n+1th elements in the vector d(n+1), and calculate the middle The kth row of the variable matrix Y, namely

得出所述中间变量矩阵Y的后M-D _p列，设置循环变量k从D _p+1逐一增加到M，在第k次循环中，计算所述中间变量矩阵Y的第k行，即Y(k,:)＝I(k,:)L(k,1:k-1)Y(1:k-1,:)；以及 _{The last MD p} column of the intermediate variable matrix Y is obtained, and the loop variable k is set _{to increase from D p} +1 to M one by one. In the kth loop, the kth row of the intermediate variable matrix Y is calculated, that is, Y( k,:)=I(k,:)L(k,1:k-1)Y(1:k-1,:); and

得到逆矩阵
定义循环变量k从N逐一递减到1，在第k次循环中，定义f取变量M-D _p和k+1中的较大者，求解逆矩阵
的第k行，即

Get the inverse matrix
Define the loop variable k to decrease one by one from N to 1, in the kth loop, define f to take _{the larger of the variables MD p} and k+1, and solve the inverse matrix
The kth line of
一种正交时频空OTFS***线性均衡装置，其特征在于，包括：A linear equalization device for an orthogonal time-frequency space OTFS system, which is characterized in that it comprises:

有效信道矩阵确定模块，用于确定OTFS***在矩形窗限制条件下的时延-多普勒域的有效信道矩阵；The effective channel matrix determination module is used to determine the effective channel matrix of the OTFS system in the time delay-Doppler domain under the restriction of the rectangular window;

评估矩阵确定模块，用于根据上述有效信道矩阵确定线性均衡评估矩阵；以及The evaluation matrix determination module is used to determine the linear equalization evaluation matrix according to the above effective channel matrix; and

均衡模块，用于根据上述线性均衡评估矩阵对接收的采样信号进行均衡。The equalization module is used to equalize the received sampling signal according to the linear equalization evaluation matrix.
一种电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述程序时实现如权利要求1至8任意一项所述的线性均衡方法。An electronic device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, wherein the processor executes the program as described in any one of claims 1 to 8. The linear equalization method described.
一种计算机可读存储介质，其特征在于，其上存储有计算机指令，在处理器执行上述计算机指令时实现如权利要求1至8任意一项所述的线性均衡方法。A computer-readable storage medium, characterized in that computer instructions are stored thereon, and the linear equalization method according to any one of claims 1 to 8 is realized when the processor executes the computer instructions.